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Re: distinguishability - in context, according to definitions
Posted:
Feb 15, 2013 8:44 AM
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In <oPydnQ9MUcW1vIPMnZ2dnUVZ_s6dnZ2d@giganews.com>, on 02/15/2013
at 05:50 AM, fom <fomJUNK@nyms.net> said:
>As this part of the construction had been
>motivated by the axiom of regularity in
>set theory, it is intuitively reasonable
>to think of a letter as "a collection
>of letters" although I suspect many will
>find that objectionable.
Use of naive set theory leads to paradoxes. If you are using any
mainstream set theory, e.g., ZFC, then no set is an element of itself.
There are theories where you could get away with that, e.g., NF, but I
suspect that you would find them awkward. More to the point, having a
letter be a collection of letters would violate the very axiom of
regularity that you cite as your motivation.
Things like that are more reasonable in Mereology, about which I don't
know much, but if you're addressing issues related to set theory that
doesn't help.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
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